Problem: Solve for $x$ : $x^2 - 9x + 8 = 0$
Explanation: The coefficient on the $x$ term is $-9$ and the constant term is $8$ , so we need to find two numbers that add up to $-9$ and multiply to $8$ The two numbers $-8$ and $-1$ satisfy both conditions: $ {-8} + {-1} = {-9} $ $ {-8} \times {-1} = {8} $ $(x {-8}) (x {-1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -8) (x -1) = 0$ $x - 8 = 0$ or $x - 1 = 0$ Thus, $x = 8$ and $x = 1$ are the solutions.